J63 | Macro Paper Warehouse

Downward Rigidity in the Wage for New Hires

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Summary

Hazell and Taska use wages posted on online job vacancies — matched to job titles and establishment identifiers from Burning Glass Technologies — to measure the wage for new hires at the job level (same job title and establishment) over 2010Q1–2020Q2. They find that this measure of the wage for new hires is rigid downward and flexible upward. At the job level, the nominal posted wage changes infrequently — on average once every 5–6 quarters — and conditional on changing, is four times more likely to rise than to fall. In the cyclical dimension, job-level posted wages rise strongly when state unemployment falls but do not fall when state unemployment rises; real wages exhibit the same asymmetric pattern. These results do not appear in the average wage for new hires (which aggregates across all job types), because time-varying job composition inflates the variance of average wages and raises standard errors roughly twentyfold relative to job-level regressions — explaining why prior work using worker-level survey data found no evidence of downward rigidity. A Heckman (1979) selection correction for firms’ selection into vacancy posting suggests that selection bias in the job-level regression is moderate. The findings provide direct empirical support for models in which downward wage rigidity for new hires — specifically at the job level — amplifies unemployment fluctuations and generates asymmetric unemployment dynamics.

In depth

Q1. Q: What is the central empirical claim of the paper?

A: At the job level — defined as the same job title within the same establishment — the wage posted for new hires is rigid downward and flexible upward. It changes infrequently and, conditional on changing, rises far more often than it falls; and it responds to falls in unemployment but not to rises in unemployment.

Q2. Q: What data does the paper use, and what defines a “job”?

A: The paper uses the Burning Glass Technologies dataset of wages posted on online vacancies, covering January 2010 to June 2020. A “job” is a job title within an establishment whose wages are paid at a given frequency (e.g., hourly or annual). The data come from the near-universe of online job postings — roughly 40,000 sources — and the main regression sample consists of jobs that post wages, have job title and establishment information, and post vacancies in multiple quarters, yielding approximately 3.05 million vacancies, representing about 0.8% of total US vacancies.

Q3. Q: How do the authors validate that posted wages measure the wage for new hires?

A: They construct a measure of the wage for new hires from the Current Population Survey (CPS) — workers switching jobs or entering from unemployment — at the state, industry, and occupation level. Regressing log CPS wages on log Burning Glass wages (using an IV split-sample procedure to correct for attenuation bias) yields a coefficient close to 1 across specifications and levels of aggregation, indicating that average posted wages move roughly one-for-one with average wages for new hires in representative survey data.

Q4. Q: How is the frequency of wage change estimated?

A: Because wages are not observed in quarters without a vacancy posting, the authors adapt a constant-hazard model from the price-setting literature (following Nakamura–Steinsson and Klenow–Kryvtsov). The latent wage evolves stochastically between postings; the observed wage is treated as a draw from this process. The quarterly probability of wage change is estimated at 0.17–0.19 across specifications, implying implied durations of unchanged wages of 4–5 quarters.

Q5. Q: What is the asymmetry in the direction of wage changes?

A: In the unweighted baseline, the quarterly probability of a wage decrease is 0.04, whereas the probability of a wage increase is 0.12 — roughly a three-to-one ratio in probabilities, summarized in the paper’s abstract as wages being “four times more likely to rise than to fall.” The distribution of non-zero wage changes also shows a pronounced pile-up of small positive changes relative to small negative changes, consistent with a downward constraint on wage setting.

Q6. Q: What is the first piece of cyclical evidence for downward rigidity?

A: A binned scatterplot (Figure 1) of job-level wage growth against state-level quarterly changes in unemployment shows a strong, roughly linear relationship when unemployment is falling — wages rise with falls in unemployment, both for small and large declines. When unemployment rises, however, wages do not fall — neither for small nor for large increases in unemployment. This asymmetry is robust to regression-based analysis and to identified labor demand shocks.

Q7. Q: Are real wages also rigid downward?

A: Yes. The paper reports that real wages (nominal posted wages deflated) are also rigid downward and flexible upward, mirroring the pattern for nominal wages.

Q8. Q: What is the job-composition problem, and why does it matter?

A: The average wage for new hires — the object measured in most prior work — aggregates across all job types that are actively hiring. If the composition of jobs hiring shifts over the business cycle (e.g., the share of lower-wage jobs rises in recessions), then average wages can fall even if no individual job cuts its wage, and can stay flat or rise even if every job cuts its wage. Job composition therefore confounds cyclicality estimates based on average wages. By tracking the same job title at the same establishment across successive vacancies, the authors purge wage changes driven by shifting composition.

Q9. Q: Why did prior work find no evidence of downward rigidity for new hires?

A: Prior work used worker-level survey data (e.g., Bils 1985; Pissarides 2009 survey) that controls for worker characteristics but averages across jobs — the average wage for new hires. The volatility of job composition inflates the variance of this average measure. In the Burning Glass data, standard errors from regressions using average wages are roughly twenty times larger than those from job-level regressions, making it impossible to detect downward rigidity even if it exists. Point estimates in prior work suggested procyclicality but were too imprecise to exclude downward rigidity.

Q10. Q: How does this paper relate to Gertler, Huckfeldt, and Trigari (2020) and Grigsby, Hurst, and Yildirmaz (2021)?

A: Both papers attempt to control for job composition at the worker level. Gertler et al. focus on wages of workers hired from unemployment (less affected by composition than all new hires) and find weakly procyclical wages. Grigsby et al. use rich payroll data and worker-level matching to control for composition and also find weakly procyclical wages. The present paper complements these by using job-level data that directly purges composition without relying on worker characteristics, and adds evidence on the asymmetry of rigidity (not just average procyclicality).

Q11. Q: What is the role of the Heckman selection correction?

A: If firms select into vacancy posting depending on business-cycle conditions, the sample of observed posted wages may be non-random, biasing job-level wage-cyclicality estimates. The authors implement a standard Heckman (1979) two-step selection correction. The correction suggests that selection bias in the job-level regression is moderate — it does not overturn the finding of downward rigidity.

Q12. Q: What are the four main caveats the authors acknowledge?

A: (1) The main sample is small — 0.8% of US vacancies — though the authors show it is broadly representative on observables and that wages track representative survey data. (2) The paper measures rigidity only for jobs that post wages; jobs that do not post wages might be more flexible, though the share of vacancies posting wages does not decline during contractions. (3) Posted wages may differ from realized (bargained) wages; however, wages are rigid even in occupations where bargaining is uncommon. (4) The Pandemic Recession is the main contractionary episode in the sample, and it involved labor supply shocks as well as demand shocks; the authors address this through identified labor demand shock regressions and by ending the sample in June 2020.

Q13. Q: What are the implications for models of unemployment fluctuations?

A: In the Diamond–Mortensen–Pissarides search model, Pissarides (2009) emphasizes that the wage for newly hired workers — not continuing workers — is the relevant margin for unemployment fluctuations. Shimer (2005) showed the standard calibration produces too-small unemployment fluctuations; wage rigidity for new hires can resolve this. The paper’s finding of downward-but-not-upward rigidity additionally supports models (e.g., Dupraz, Nakamura, and Steinsson, 2020) in which this asymmetry generates asymmetric unemployment dynamics — unemployment rises sharply in contractions but falls more slowly in expansions.

Q14. Q: How do wages for new hires compare with wages for continuing workers in terms of rigidity?

A: The paper finds approximate parity. The implied duration of unchanged wages from the job-level posted wage data (4–5 quarters) is similar to estimates for continuing workers in the prior literature. This is perhaps surprising because wages could in principle be more flexible for new hires than continuing workers — firms might cut wages for new hires even while insuring continuing workers (Beaudry and DiNardo, 1991). The results instead suggest that internal equity concerns (Bewley, 2002) or other forces produce similar rigidity for both groups.

Key Concepts

Job level wage: The wage across successive vacancies posted by the same job title at the same establishment. This is the unit of observation in the paper’s main analysis and the object for which downward rigidity is documented. Distinct from the average wage for new hires (which aggregates across all job types).

Downward rigidity (as used in this paper): An empirical pattern in which wages at the job level do not fall during contractions — they do not respond to rising unemployment — while rising during expansions in response to falling unemployment. The claim is descriptive: the data show wages do not fall; the paper does not structurally identify the mechanism enforcing this floor.

Job composition problem: The bias introduced when measuring cyclicality of the average wage for new hires using data that aggregates across different types of jobs. If the mix of job types hiring shifts with the business cycle, average wages can change even when no individual job changes its wage, and can mask individual-job wage changes. Job-level data resolve this by holding the job fixed.

Burning Glass Technologies dataset: A database of wages posted on online job vacancies, drawn from approximately 40,000 online sources (job boards and company websites), covering the near-universe of US online vacancies. The paper’s main regression sample uses the subset with posted wages, job title, establishment identifiers, and multiple quarters of postings, spanning January 2010 to June 2020.

Constant hazard model (wage change frequency): An estimation procedure adapted from the price-setting literature to recover the quarterly probability of wage change from a dataset in which wages are only observed when a vacancy is posted. The latent wage evolves with a constant hazard of change between observations; observed wage changes identify the hazard rates for increases and decreases separately.

Average wage for new hires: The mean wage across all workers newly entering employment (or across all new-hire jobs), used in prior work (Bils 1985 and related). Does not control for job composition. Shown in this paper to exhibit no detectable downward rigidity, with standard errors roughly twenty times larger than in job-level specifications — because job composition variance inflates the residual variance.

Heckman selection correction: A two-step procedure (Heckman 1979) to correct for the possibility that firms that post vacancies — and post wages — are a selected sample that differs systematically across the business cycle. The paper applies this to assess whether selection into vacancy posting biases the job-level wage-cyclicality estimates; the correction suggests bias is moderate.

Summary based on LSE Research Online accepted version (accepted manuscript, covers full paper including introduction, data, and Section 3; extraction terminated at line 595 before Sections 4–5). AI-assisted, human review pending.

Education and the Margins of Cyclical Adjustment in the Labor Market

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research question. This paper asks how the cyclical sensitivity of wages varies with workers’ educational attainment, what mechanisms drive the differences, and what the welfare consequences are of ignoring this heterogeneity. The starting point is a well-known asymmetry: less-educated workers have much higher and more volatile job separation rates, yet the standard macroeconomic literature has treated wages as roughly acyclical for a representative worker. Doniger asks whether this employment-centric picture is incomplete—and finds that it is, in a direction opposite to what the employment pattern would suggest.

Data and methodology. The paper uses two primary data sources: the National Longitudinal Survey of Youth 1979 (NLSY), which provides detailed job histories enabling identification of current and completed employer tenure, and the Current Population Survey (CPS) from 1995 to 2020, used both for employment flow statistics and, via biennial Job Tenure Supplements, for replication of the main wage findings. The sample is restricted throughout to males with 0–30 years of potential experience, following the conventions of the user-cost-of-labor (UCL) literature (Kudlyak, 2014; Basu and House, 2016). Workers are grouped into three educational categories: less than high school, high school or some college, and bachelor’s degree or more.

A key methodological contribution is a new, more parsimonious estimator for the cyclical sensitivity of the UCL. Rather than the multi-step indicator-variable approach of Kudlyak (2014), the paper recovers the UCL sensitivity from interaction terms between a flexible function of tenure and the cyclical position at the time of hiring, estimated within an augmented Mincer regression. This estimator admits higher-frequency identification, enables transparent inference via the delta method, and facilitates nonparametric impulse response estimation via the Jorda (2005) local projection method. Cyclical position is measured primarily as the deviation of the unemployment rate from an HP-filtered trend (lambda = 100,000), with robustness checks using the Hamilton (2018) filter and GDP-based detrending.

Main findings — employment. Monthly separation rates from the CPS (1995–2020) show that workers with less than a high school degree separate at a rate of 9.4 percent per month, more than twice the 3.4 percent rate for workers with a bachelor’s degree or more, regardless of cyclical position. The volatility of the separation rate (measured by the time-series standard deviation) is also larger for the least educated (1.7) than for the most educated (0.6). All sub-components of separation-to unemployment, to inactivity, and job-to-job transitions-exhibit the same ordering. In response to a 100 basis point monetary policy contraction (Romer and Romer, 2004 shocks), employment of workers with less than a high school education falls significantly, while employment of college graduates or more is statistically unaffected.

Main findings — wages. Using the NLSY, the cyclical sensitivity of the UCL to a 1 percentage point deviation of the unemployment rate from trend is estimated at approximately −15.5 percent for workers with a bachelor’s degree or more, −4.9 percent for high school or some college workers, and −1.4 percent (statistically indistinguishable from zero) for workers without a high school degree. In contrast, average hourly earnings (AHE) show much smaller and more compressed differences across education groups (−1.4, −1.1, and −1.0 percent respectively). The pattern of increasing procyclicality with education holds for new hires’ wages (NHW) as well but is considerably less stark than for the UCL. Replication in the CPS confirms the ordering: UCL sensitivities are −7.0 percent for college graduates, −2.9 percent for high school or some college, and effectively zero for those without a high school degree.

Mechanism. Counterfactual decompositions show that differences in the cyclical sensitivity of the wage-tenure profile—not just differences in job duration (separation rates)-account for the vast majority of the divergence across education groups. When separation rates are held constant across groups, the UCL sensitivity of the college-educated falls from -15.5 to −13.0 percent; when wage-tenure profile sensitivities are held constant, it falls to −6.3 percent, and the ordering across groups largely disappears. This finding is consistent with implicit contracting theory (Thomas and Worrall, 1988): longer expected employment durations for the more educated make it optimal to defer a greater share of the wage response to shocks over time, rendering near-term rigidities functionally less binding and producing more persistent effects of hiring-period conditions on subsequent wages.

Robustness. After controlling for cyclical sorting in match quality using the Hagedorn and Manovskii (2013) proxies (cumulated market tightness during tenure and leading up to the present job), the UCL sensitivity for college graduates falls modestly to −12.4 percent, confirming that match-quality composition effects account for only a minority of the documented pattern. The monetary policy shock analysis (Romer-Romer shocks identified from Greenbook forecast errors) yields a 35 percent decrease in the UCL for the most educated at the two-year horizon following a 100 basis point contraction, with no discernible effect for the least educated.

Welfare consequences. Using a stylized New Keynesian model extended to two labor varieties with heterogeneous wage flexibility, the paper shows that ignoring the documented heterogeneity leads to underestimating the welfare costs of business cycle fluctuations by more than 15 percent under the baseline calibration (unit Frisch elasticity and unit elasticity of intertemporal substitution). Conditional on this model, the welfare loss due to fluctuations for the least educated is more than 15 times larger than for the most educated. The paper explicitly notes this is a conservative lower bound, because the model assumes pooled household consumption, and admitting idiosyncratic consumption risk would disproportionately burden less-educated workers who bear adjustment on the extensive (employment) rather than intensive (wage) margin.

In depth

Q1. What is the user cost of labor (UCL), and why does the paper use it rather than average hourly earnings or new hires’ wages?

The UCL, formalized by Kudlyak (2014), is the present discounted value of wage payments an employer expects to make to a worker over the duration of the employment relationship, net of the continuation value of retaining that worker. It equals the new hire’s wage plus the expected wage wedge—the discounted stream of future wage differences between workers hired in the current period versus workers hired one period later. Unlike average hourly earnings or new hires’ wages, the UCL captures the persistent effects of macroeconomic conditions at the time of hiring on all future remitted wages, making it the appropriate allocative wage concept from a macroeconomic standpoint. The paper documents that AHE understates the cyclicality of wages for all groups but especially for the most educated, because AHE omits the highly cyclically sensitive expected wage wedge that characterizes college-educated employment relationships.

Q2. How does the paper’s new estimator for the cyclical sensitivity of the UCL differ from the existing method, and what does this enable?

The existing Kudlyak (2014)/Basu and House (2016) method recovers the UCL by estimating a very large set of date-of-hire x current-date indicator interactions, constructing a time series of the UCL, and then analyzing that series—a multi-step procedure that loses covariances across steps and makes cross-sectional disaggregation or high-frequency identification impractical. The new method instead estimates the UCL sensitivity directly from coefficients on the interaction between a flexible tenure function and the cyclical position at hiring, estimated within a single augmented Mincer regression. The UCL semi-elasticity is recovered analytically from these coefficients via a formula that sums discounted weighted differences in the tenure-interaction coefficients across the tenure horizon. This single-step approach allows transparent inference via the delta method, enables fully interacted specifications for heterogeneous subgroups, permits the hiring-date frequency (e.g., weekly in NLSY) to differ from the wage observation frequency (annual or biannual), and permits estimation from repeated cross-sections—all of which were infeasible in the prior approach.

Q3. What are the quantitative magnitudes of the education gradient in UCL cyclicality, and how do they compare across wage measures?

Using the NLSY with unemployment deviations from HP-filtered trend as the cyclical indicator: the UCL sensitivity is −15.5 percent (se 3.86) for workers with a bachelor’s degree or more, −4.9 percent (se 1.52) for high school or some college, and −1.4 percent (se 2.48, statistically insignificant) for those without a high school degree. By contrast, new hires’ wages show sensitivities of −3.4, −1.8, and −1.2 percent respectively, and average hourly earnings show −1.4, −1.1, and −1.0 percent. The gradient is largest and most statistically significant for the UCL, indicating that the bulk of the education gap in cyclical wage sensitivity operates through the persistent effect of hiring-period conditions on subsequent wages rather than through the contemporaneous wage alone.

Q4. What mechanism accounts for the UCL gradient — differential job durations or differential sensitivity of the wage-tenure profile?

The paper decomposes the UCL into the new hire’s wage and the expected wage wedge, and performs counterfactual exercises holding either separation rates or wage-tenure profile sensitivities constant across education groups (Table 3). Holding separation rates constant while allowing wage-tenure profiles to differ reduces the college-educated UCL sensitivity only modestly, from -15.5 to −13.0 percent; holding wage-tenure profile sensitivities constant while allowing separation rates to differ reduces the college-educated sensitivity to −6.3 percent and compresses the education gradient substantially. Thus, differential sensitivity of the wage-tenure profile—the degree to which wages continue to respond to hiring-period conditions over the course of the job-is the primary driver of the UCL gradient, with differential separation rates playing a secondary but non-trivial role. This finding confirms the prediction of Thomas and Worrall (1988) that lower separation rates support greater use of deferred payment and intertemporal risk sharing in optimal wage contracts.

Q5. How does the paper rule out cyclical sorting in match quality as the explanation for the UCL gradient?

Workers hired during recessions may be of systematically lower match quality, producing persistently lower wages not because wages are more cyclically sensitive for the same quality match but because recession hires are worse matches. Using the Hagedorn and Manovskii (2013) proxies for match quality - cumulated market tightness during the worker’s tenure on the present job (mjob) and on all prior jobs leading to it (mctj) - the paper augments the wage regression with full interactions between these proxies and the tenure-cyclicality terms. After controlling for match quality, the UCL sensitivity for college graduates falls from -15.5 to −12.4 percent (se 5.56); the point estimate remains large, statistically significant, and well above the estimates for lower-education groups. Figure 4 shows that match-quality adjustment primarily affects the first two years of the wage-tenure profile, after which the bias from cyclical sorting fades, confirming that scarring in remuneration for college graduates hired in recessions persists beyond what sorting can explain.

Q6. What do monetary policy shocks reveal about the education gradient in wage sensitivity?

Monetary policy shocks (identified from Greenbook forecast errors as in Romer and Romer, 2004) subject all labor markets to the same aggregate demand shock simultaneously, providing a cleaner test of differential responsiveness than cyclical regressions that may conflate demand composition and supply factors. Using Jorda (2005) local projections, a 100 basis point monetary policy contraction is associated with a 35 percent decrease in the UCL for workers with a bachelor’s degree or more at the two-year horizon, with statistically insignificant effects on the UCL of workers without a high school degree. The employment results are symmetric: less-educated workers’ employment falls significantly after a monetary contraction, while college-educated workers’ employment is unaffected. This cross-validation using monetary policy shocks supports the main thesis that more-educated workers absorb aggregate demand variation through the wage margin, while less-educated workers absorb it through the employment margin.

Q7. How does acyclical wages for the least educated affect interpretation of the existing macro literature on wage rigidity?

The aggregate finding of Kudlyak (2014) and Basu and House (2016)-that the UCL is more procyclical than new hires’ wages or average hourly earnings, casting doubt on wage rigidity as an amplification mechanism—holds only for educated workers. The paper finds that the UCL for workers without a high school degree is statistically acyclical by all three wage measures. This result restores a potential role for nominal wage rigidity in generating amplification and persistence of shocks for less-educated labor markets, including in the Diamond-Mortensen-Pisarides class of search models criticized by Kudlyak (2014) and in New Keynesian models criticized by Basu and House (2016). The paper therefore reconciles the literature on wage rigidity with the empirical finding of cyclical employment volatility concentrated among the less educated.

Q8. What is the welfare calculation, and what are its key results and limitations?

The welfare exercise uses a parsimonious New Keynesian model with two labor varieties (capturing more- and less-educated workers) and price and wage rigidities. The model is extended to admit heterogeneous wage flexibility, and the welfare costs of fluctuations are evaluated following the second-order approximation method of Gali et al. (2007). Under the baseline calibration (unit Frisch elasticity, unit elasticity of intertemporal substitution), the heterogeneous-worker economy incurs welfare costs of fluctuations that exceed those of the output-gap-equivalent representative agent economy by more than 15 percent. The welfare loss of the least-educated workers is more than 15 times that of the most educated. The paper explicitly characterizes this as a conservative lower bound: the model assumes pooled household consumption (within varieties), which implies equal consumption sensitivity across education groups, whereas in reality less-educated workers face income loss on the extensive margin without the wage smoothing available to the more educated. Relaxing this assumption, as in Krusell et al. (2009), could yield welfare losses an order of magnitude larger.

Q9. What does the CPS replication add, and what are its limitations relative to the NLSY baseline?

The CPS replication (Table 7) confirms the main ordering: UCL sensitivities are −7.0, −2.9, and approximately 0 percent for college graduates, high school or some college, and less than high school respectively. This rules out the concern that the NLSY findings are artifacts of the single aging cohort that characterizes the NLSY 1979. However, the CPS must be treated as a repeated cross-section because the tenure data are only available biennially and individual-level panel linkage across tenure supplement waves is infeasible. As a result, the CPS estimates cannot include individual fixed effects and must rely more heavily on observable controls (industry, occupation) to absorb cyclical variation in workforce composition. The CPS also precludes the match-quality controls of Hagedorn and Manovskii (2013). Despite these limitations, the main qualitative and directional findings replicate.

Q10. What policy implications does the paper draw for monetary policy?

The paper argues that because less-educated workers bear adjustment to aggregate demand shocks disproportionately through the employment margin while their wages are acyclical, welfare assessments that focus on the aggregate output gap underweight the costs borne by less-educated workers. The paper suggests that re-optimizing the monetary policy rule to account for documented heterogeneity would entail placing greater weight on the unemployment rate of the least-educated when measuring the output gap. More broadly, the K-shaped nature of labor market adjustment across education groups — wage scarring for the educated versus employment volatility for the less educated - implies that policies targeting either margin in isolation will miss welfare costs concentrated in the other group.

Key Concepts

User Cost of Labor (UCL). The allocative wage from the employer’s perspective, defined as the present discounted value of expected future wage payments to a worker hired at date t, net of the continuation value of retaining that worker in the next period. Formally, UCL_t = w_{t,t} + E_t[sum beta^j(1-s)^j (w_{t+j,t} - w_{t+j,t+1})], decomposing into the new hire’s wage and the expected wage wedge. In this paper’s usage, the UCL is the appropriate measure of the cyclical impact of shocks on labor costs because it captures persistent effects of hiring-period conditions on the entire subsequent wage sequence, not just the contemporaneous wage.

Expected Wage Wedge (EWW). The component of the UCL beyond the new hire’s wage: the discounted stream of differences between wages a worker hired at date t will receive in future periods and the wages a worker hired one period later would receive in those same future periods. The EWW is non-zero whenever wages are history-dependent - i.e., whenever current macroeconomic conditions at the time of hiring affect future remitted wages. The paper finds that the EWW is larger, more negative, and more persistent for more-educated workers conditional on being hired during a cyclical downturn.

Self-enforcing implicit wage contract. A labor contract in which the sequence of remitted wages is not pinned down period-by-period by spot-market forces but instead reflects an intertemporal risk-sharing arrangement between employer and worker that is sustained by the mutual benefit of the ongoing employment relationship. In this paper’s framework (drawing on Thomas and Worrall, 1988), lower separation rates make longer planning horizons feasible, which in turn expands the scope for deferring wage adjustments across time - effectively allowing more-educated workers and their employers to smooth the effects of cyclical shocks over longer horizons than is possible for less-educated workers with shorter expected job durations.

Cyclical sorting / match quality bias. The compositional concern that workers hired during recessions may be of systematically different (in this context, lower) match quality than those hired during booms, so that the persistent wage depression observed for recession hires could reflect poor match quality rather than cyclically sensitive wages for equivalent-quality matches. The paper uses the Hagedorn and Manovskii (2013) proxies - cumulated labor market tightness during the current job and prior employment history - to control for cyclical variation in match quality and assess the residual sensitivity of the UCL for average-quality matches.

Extensive versus intensive margin of labor market adjustment. The distinction between adjustment through changes in the number of workers employed (extensive margin: hiring and separation) versus adjustment through changes in wages or hours conditional on employment (intensive margin). A central finding of the paper is that less-educated workers bear cyclical adjustment disproportionately on the extensive margin (more volatile separation rates, employment losses following monetary contractions) while their wages are acyclical, whereas more-educated workers exhibit the reverse: stable employment but highly cyclically sensitive wages, especially as measured by the UCL.

Wage scarring. The persistent negative effect of hiring-period macroeconomic conditions on wages throughout the subsequent employment spell, beyond what is explained by contemporaneous market conditions. In this paper’s context, wage scarring is concentrated among more-educated workers: being hired when the unemployment rate is one percentage point above trend is associated with wages that remain depressed for several years, with the depression being larger and more persistent for college-educated workers than for those with less education. This is demonstrated via the expected wage wedge profiles in Figure 3 and is confirmed to survive controls for match-quality sorting.

Output-gap-equivalent representative agent economy. A conceptual benchmark constructed in the paper’s welfare analysis: a single-worker-type New Keynesian economy whose wage and labor supply elasticities are set equal to the output-elasticity-weighted averages of the two labor variety types in the heterogeneous economy. The paper shows that the heterogeneous-worker economy and this representative-agent benchmark produce identical aggregate output gap and price level paths (under Cobb-Douglas production, earnings elasticities are identical across varieties), but welfare diverges because period utility is more volatile for the variety with more rigid wages. The 15 percent excess welfare cost of the heterogeneous economy relative to this benchmark is the paper’s headline welfare result.

Firm dynamics and random search over the business cycle

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

How do aggregate economic fluctuations reallocate workers across the firm productivity distribution over the business cycle? In particular, to what extent do recessions impede workers’ movement up the job ladder toward more productive firms?

Model and Methodology

The paper develops a tractable random search model combining three features that had not previously been integrated in a single quantitative framework: (i) firm dynamics driven by idiosyncratic productivity shocks, with endogenous entry and exit; (ii) on-the-job search, generating a job ladder in which workers gradually move toward more productive firms; and (iii) aggregate productivity shocks. Multi-worker firms post employment contracts, choose hiring rates, and decide whether to continue or exit. The key tractability result — called “size-independence” (Result 1) — shows that, under a constant-returns hiring cost technology, firms’ optimal policies (contract value, hiring rate, exit decision) are all independent of firm size, so the relevant state space reduces from the full joint distribution of firm productivity and size to the employment-weighted distribution of firm productivity alone. A further result (“rank-monotonic equilibrium,” Result 2) guarantees, under a sufficient convexity condition on hiring costs (hc’’(h)/c’(h) ≥ 1), that the optimal employment contract is increasing in firm productivity, so the job ladder maps one-for-one onto the firm productivity ladder. The optimal wage contract then admits a closed-form solution.

The model is calibrated to British data for 1997–2018. Worker-level transition rates (unemployment-to-employment, employment-to-unemployment, and job-to-job) are drawn from the British Household Panel Survey (BHPS). Firm-level data on labor productivity (value added per worker) and employment costs per worker come from the Annual Respondents Database (ARD) and Annual Business Survey (ABS), merged with the Business Structure Database (BSD). The numerical solution adapts ideas from Krusell and Smith (1998), approximating the employment-weighted productivity distribution by a small set of moments and parameterizing value functions as polynomials in the aggregate state; standard linearization methods are inapplicable because endogenous firm entry and exit introduces a discontinuity in value functions.

Main Findings

Model validation via the OP decomposition. The paper’s central validation exercise uses the Olley-Pakes (OP) decomposition of a labor productivity index constructed from firm-level data. The aggregate employment-weighted labor productivity index is decomposed into (a) the unweighted average firm productivity and (b) an interaction term (the “OP term”), which captures the covariance between employment shares and productivity — i.e., how well workers are allocated to productive firms. In the British firm-level data, approximately 20 percent of the variance of the aggregate labor productivity index is accounted for by this interaction (OP) term, with the remaining ~80 percent attributable to the unweighted average of firm productivity. The baseline model, with this moment untargeted, successfully replicates this 80/20 split. By contrast, the leading benchmark model of Moscarini and Postel-Vinay (2016) (MPV2016), calibrated to the same British data, attributes nearly all of the variance of labor productivity to the OP/worker reallocation term, grossly overstating the importance of job-ladder dynamics.

Structural decomposition of labor productivity. Using the calibrated baseline model to decompose the variance of aggregate labor productivity over the post-war British business cycle (“GDP shocks” going back to 1955), the baseline model attributes approximately 30 percent to the direct effect of the aggregate productivity shock, approximately 50 percent to changes in the distribution of active firms (the “firm ladder” or firm selection component), and approximately 20 percent to the worker reallocation component (the OP interaction term). This result is robust to an alternative calibration with a lower curvature of the hiring cost function (c1 = 1).

Persistence and mechanisms. The impact of recessions on the job ladder is persistent: while the aggregate productivity shock is typically close to its pre-recession value four years after a typical recession onset, the overall allocation of workers to firms remains clearly worse relative to the pre-recession level at that same horizon. The Great Recession, viewed through the lens of the model, is a large but not unusually large recession.

Firm selection with multiple aggregate shocks. An unexpected finding concerns the direction of firm selection. With a single aggregate productivity shock, the model generates a standard “cleansing” mechanism: negative shocks raise the firm exit threshold, so surviving firms are on average more productive. However, when additional shocks to the exogenous separation rate (δ) and hiring cost scale (c0) are included — as required to match the volatility of labor market flows — firm selection instead amplifies the decline in labor productivity. The mechanism is a general equilibrium one: a higher separation rate lowers the optimal wage contract (since greater separation risk is passed on to workers), which in turn lowers the entry-exit threshold. Less productive firms become viable because their employees face higher unemployment risk and therefore accept lower wages; moreover, a larger pool of unemployed workers makes it easier for low-productivity firms to recruit.

Wage flexibility tension. The model implies a pass-through elasticity of wages to productivity shocks of approximately 0.7, well above the 0.05–0.2 range typically found empirically.

Scope Conditions

All calibration and quantitative results pertain to Britain for the period 1997–2018 (firm-level data) and 1955–2018 (GDP-based aggregate shocks). The model abstracts from decreasing returns to scale in production and from nominal rigidities. The tractability results rely on specific assumptions about the hiring cost function; the rank-monotonicity condition requires sufficient convexity (hc’’(h)/c’(h) ≥ 1).

In depth

Q1. What is the central tractability result and why does it matter for computational feasibility?

A: Result 1 (“size-independence”) shows that, because both the production technology and the hiring cost function are constant returns to scale, the firm’s present discounted value of profits is linear in employment. As a result, per-worker profits are independent of firm size, and optimal firm policies — the hiring rate, the contract value offered to workers, and the continuation/exit decision — all depend only on the firm’s current productivity, not on its size. This collapses the state space from the full joint distribution of firm productivity and employment size to the employment-weighted measure of firm productivity Lt(p), a uni-dimensional object. Without this result, the model would require tracking the entire joint firm distribution, making it computationally intractable.

Q2. What is a rank-monotonic equilibrium (RME) and what conditions guarantee it?

A: An RME is a recursive equilibrium in which the optimal contract offered by a firm is weakly increasing in that firm’s current productivity realization, for all aggregate states. Result 2 provides sufficient conditions: (i) the Markov process for firm-specific productivity satisfies first-order stochastic dominance (more productive firms today are more likely to be more productive tomorrow), (ii) the distribution of offered contracts is everywhere differentiable (ruling out mass points), and (iii) the hiring cost function satisfies hc’’(h)/c’(h) ≥ 1 — a sufficient convexity condition. The economic interpretation of the convexity condition is that firms must find retention (offering higher wages) sufficiently costly relative to new hiring that more productive firms optimally choose to use the wage margin to limit quits. The baseline calibration yields c1 ≈ 5.9 (so costs are highly convex in the hiring rate), though results are also reported for the minimum permissible c1 = 1.

Q3. What does the optimal employment contract look like in a rank-monotonic equilibrium, and what does it reveal about rent extraction?

A: In an RME, the optimal contract V(p,ω,L) is a weighted average of the value of unemployment U(ω,L) and the firm-workers’ joint surplus S(p,ω,L), where the weights are determined endogenously by the employment-weighted measure of firm productivity L. Specifically, the contract integrates the surplus of all firms with productivity below p, weighted by the share of employed workers at those firms, and divided by the mass of job seekers willing to accept the contract. As the employed workers’ relative search intensity s approaches zero, the contract converges to the value of unemployment — workers receive no rents. The endogenous bargaining weight evolves with the aggregate state over the business cycle, unlike standard Nash bargaining models with a fixed exogenous weight.

Q4. What firm-level moments are used to calibrate the steady-state model, and what is the logic behind the parameter-moment mapping?

A: Eight moments are targeted. From the BHPS worker data: the average UE rate (0.058) pins down the scale of hiring costs c0; the average EU rate (0.003) pins down the exogenous separation rate δ; and the average EE (job-to-job) rate (0.016) pins down the relative search intensity s. From the firm-level ARD/BSD data: average firm size (12.1 employees) pins down the entry probability µ; the share of job destruction from firm exits (0.526) disciplines the flow value of unemployment b; the autocorrelation of firm employment ln(n) (0.949 annually) disciplines the persistence of idiosyncratic productivity ρp; the interquartile range of firm-level labor productivity (1.129 log points) disciplines the volatility of idiosyncratic shocks σp; and the regression coefficient of firm employment growth on lagged labor productivity (0.136) disciplines the curvature of hiring costs c1. The baseline calibration fits all eight moments closely.

Q5. How does the calibrated model match non-targeted moments, and what does this establish?

A: The model generates several realistic features not targeted in calibration. It produces a realistic Pareto tail for the employment-size distribution (Pareto tail exponent of 1.033 in the model vs. 1.066 in the data), which arises from the combination of size-independent growth rates and firm entry and exit — conditions identified in the literature as generating power law distributions. The model also matches the dispersion of employment costs per worker across firms (capturing about 70 percent of the interquartile range of ECi,t), the slope of a regression of employment costs on labor productivity (model: 0.685 vs. data: 0.704), and the slope of a regression of employment growth on employment costs (model: 0.162 vs. data: 0.131). These non-targeted matches provide independent validation of the model’s wage-determination mechanism.

Q6. Why is a single aggregate productivity shock insufficient to match labor market fluctuations, and what additional shocks are needed?

A: With a single aggregate productivity shock calibrated to match the autocorrelation and standard deviation of log GDP, the model generates labor market fluctuations that are roughly an order of magnitude smaller than in the data. For example, the standard deviation of the EU transition rate is 4.1×10⁻⁴ in the single-shock model versus 2.3×10⁻³ in the data. Adding a discount rate shock (ω,r) partially helps but still leaves the job-finding rate (UE) more than 50 percent too smooth. Adding a separation rate shock (ω,δ) substantially increases EU and UE volatility but generates insufficient EE (job-to-job) volatility. The combination (ω,δ,c0) — adding a shock to the scale of hiring costs c0 — brings the standard deviations of EU and UE close to the data (2.0×10⁻³ and 4.0×10⁻⁴ vs. data 2.3×10⁻³ and 2.7×10⁻⁴), though the model still generates slightly under half the observed volatility in EE rates. This combination is the baseline for the quantitative analysis.

Q7. What is the OP decomposition, how is it computed from the firm-level data, and what does it measure in the model?

A: The aggregate labor productivity index LPt is constructed from firm-level data as the employment-share-weighted average of log value added per worker across firms. The OP decomposition writes this as LPt = LPt_bar + OPt, where LPt_bar is the unweighted (simple) average of firm-level productivity and OPt is the covariance between employment shares and labor productivity (the “interaction term”). In the data, OPt increases when workers are disproportionately employed at above-average-productivity firms. In the model, LPt_bar maps onto the average (log) productivity of active firms — the support of the job ladder — while OPt maps onto the difference between the employment-weighted and the unweighted averages of firm productivity, directly measuring how high up the ladder workers are located relative to the set of active firms. Around 20 percent of the variance of LPt in the British data is accounted for by OPt, and the model replicates this.

Q8. How does the Great Recession appear in the OP decomposition, and does the model fit the decomposition during this episode?

A: During the Great Recession (2008q2–2009q3 in the UK), around 20 percent of the overall fall in the labor productivity index is accounted for by the fall in the OP interaction term, with the remaining 80 percent coming from the fall in the unweighted average firm productivity. The model, even though it does not target this decomposition in calibration, successfully matches both the average firm productivity component and the interaction (OP) component during the Great Recession. This matching holds both in the baseline calibration (c1 ≈ 5.9) and in the alternative calibration with c1 = 1. The model also matches the analogous decomposition for employment costs per worker (ECt), an additional non-targeted validation.

Q9. Why does firm selection amplify rather than cleanse in the baseline multi-shock calibration?

A: In the single-shock (productivity ω only) model, a negative productivity shock lowers surplus at all firms, raising the exit threshold pE and thus selecting out low-productivity firms — the standard “cleansing” mechanism. In the multi-shock baseline, the additional separation rate shock (δ) generates a less intuitive mechanism. A higher δ lowers the optimal wage contract (since increased separation risk is passed on to workers: ∂V/∂δ ≤ 0), which reduces the value of continued employment. This lowers the joint firm-worker surplus threshold for exit, making it viable for low-productivity firms to remain active. Moreover, the larger pool of unemployed workers (generated by the δ shock) depresses the outside option of workers and makes it easier for low-productivity firms to recruit. As a result, the entry-exit threshold pE,t falls — the set of active firms becomes less productive on average — producing a negative firm selection contribution to labor productivity and a positive (amplifying rather than cleansing) contribution to the variance of LPt.

Q10. What is the structural variance decomposition of labor productivity in the baseline model?

A: Simulating the baseline model over the post-war British business cycle (1955–2020, GDP shocks), the variance of aggregate labor productivity LPt decomposes into three structural terms: approximately 30 percent (0.296) from the direct effect of the aggregate productivity shock ln(ωt); approximately 50 percent (0.541) from changes in the average productivity of active firms E[KP bar_t(ln p)] — the “firm ladder” or firm selection component; and approximately 20 percent (0.163) from the worker reallocation component OPt = E[LP bar_t(ln p)] − E[KP bar_t(ln p)]. This decomposition implies that roughly 70 percent of fluctuations in labor productivity are driven by worker reallocation broadly defined (the firm ladder plus the interaction term), with the firm selection component being the largest single driver. The result is robust to the alternative c1 = 1 calibration (30/49/22 percent split).

Q11. How does the baseline model compare to MPV2016 in the variance decomposition?

A: In the multi-shock calibration (ω,δ,c0), the MPV2016 model calibrated to the same British data attributes approximately 97.7 percent (0.977) of the variance of LPt to the worker reallocation (OP) term, with essentially none attributed to a firm selection term (since there is no firm entry and exit in MPV2016). This is nearly five times the 20 percent share attributed to worker reallocation in the data and in the baseline model. In the single-shock (ω) calibration, both models attribute a more modest share to worker reallocation (7.2 percent for the baseline model, 0.1 percent for MPV2016 with c1=5), and the difference narrows considerably. The contrast thus stems from the interaction of firm dynamics with multiple aggregate shocks: allowing for endogenous firm entry and exit is critical to prevent the model from overstating the role of the job ladder.

Q12. How persistent is the impact of recessions on the job ladder, based on the model simulations?

A: The paper simulates the structural decomposition of labor productivity starting from each of seven post-war British recessions (defined by two consecutive quarters of negative GDP growth). On average across these recessions, the aggregate productivity shock ln(ωt) is close to its pre-recession level by four years after the recession onset. However, the overall employment-weighted average productivity E[LP bar_t(ln p)] — reflecting workers’ position on the job ladder — remains clearly below its pre-recession value at the four-year horizon, indicating persistent misallocation. The OP interaction term accounts for approximately 20 percent of the total drop in the employment-weighted productivity measure three years after a typical recession onset. Through the model’s lens, the Great Recession is a large recession but not an outlier relative to the historical distribution.

Q13. What does the counterfactual with countercyclical unemployment benefits reveal about the tradeoff between firm selection and worker reallocation?

A: When the flow value of unemployment is made countercyclical (falling in recessions, rising in expansions — mimicking US unemployment insurance extension programs), the model generates a sign reversal in the firm selection (“firm ladder”) component. With countercyclical b, the unemployment value rises in recessions, which raises the minimum wage firms must offer and raises the exit threshold pE,t: fewer low-productivity firms survive, improving the composition of active firms. However, countercyclical benefits also amplify the slowdown in job-to-job reallocation: the higher value of unemployment reduces workers’ willingness to accept job offers, and all firms cut recruitment since optimal wage contracts must rise. The OP interaction term therefore falls more sharply than in the baseline model. The counterfactual with ϵb,ω ∈ {−100, −50} finds that the positive “firm ladder” effect dominates on net, so the overall allocation of workers to firms improves relative to the baseline after a typical recession under countercyclical unemployment benefits.

Q14. What is the numerical solution method, and why are standard linearization approaches inapplicable?

A: The model is solved in two steps. First, aggregate shocks are shut down and the steady-state rank-monotonic equilibrium is solved numerically by discretizing the firm productivity process (401 grid points via Tauchen’s method) and iterating on the value function and the employment-weighted productivity measure until convergence. Second, aggregate shocks are reintroduced using a simulation-based approach adapted from Krusell and Smith (1998): the employment-weighted distribution of productivity is summarized by Nm = 2 moments (plus the unemployment rate), and the value functions are parameterized as polynomials in the aggregate state, with coefficients updated by regression until convergence. Standard linearization methods (Reiter 2009) are inapplicable because the endogenous entry-exit decision creates a kink (discontinuity) in value functions at the productivity threshold pE, making first-order approximations around the steady state inaccurate. Accuracy tests based on den Haan (2010) show that the polynomial approximation generates errors of at most 0.065 percent for value functions and at most 1 percentage point for the unemployment rate across simulation paths.

Key Concepts

1. Rank-Monotonic Equilibrium (RME) A recursive equilibrium in which the optimal state-contingent employment contract V(p,ω,L) offered by a firm is weakly increasing in the firm’s current productivity realization p, for all aggregate states (ω,L). This property implies that the job ladder maps one-for-one onto the firm productivity ladder: workers always prefer to work at more productive firms. The paper shows this property holds under a sufficient convexity condition on hiring costs (hc’’(h)/c’(h) ≥ 1) and first-order stochastic dominance of the productivity process.

2. Size-Independence The property that a firm’s optimal policies — the hiring rate h(p), the employment contract V(p), and the entry/exit decision χ(p) — are all independent of the firm’s current employment size n. This follows from constant returns to scale in production and hiring, which implies that firm profits are linear in employment. Size-independence reduces the model’s relevant state space to the employment-weighted distribution of firm productivity, enabling tractability.

3. Employment-Weighted Distribution of Firm Productivity (L_t(p)) The measure recording, for each productivity level p, the total employment at firms with productivity at most p. This is the sufficient statistic for the state of the job ladder at any point in time: combined with the aggregate shock ω, it determines all equilibrium policy functions and value functions. In the model, it replaces the full joint distribution of firm productivity and employment size that would otherwise be required.

4. OP Decomposition (Olley-Pakes Decomposition) The decomposition of the aggregate employment-weighted labor productivity index LPt into: (a) the unweighted average firm productivity LPt-bar, which summarizes the productivity of active firms (the support of the job ladder); and (b) an interaction term OPt, the covariance between employment shares and firm-level productivity, which measures how well workers are allocated across the productivity distribution (i.e., how high up the ladder workers sit given the set of active firms). In the model, (a) maps to E[KP bar_t(ln p)] and (b) maps to OPt = E[LP bar_t(ln p)] − E[KP bar_t(ln p)].

5. Contract Posting The wage-setting protocol in which each firm commits upon entry to a full state-contingent employment contract — a schedule mapping each future realization of aggregate and idiosyncratic productivity to a wage and continuation decision — and is bound by an equal treatment constraint to offer the same contract to all employees. Workers cannot renegotiate based on outside offers. This protocol produces a well-defined closed-form for the optimal contract in an RME and differs from alternating-offer bargaining (Nash bargaining) in that the bargaining weights are endogenous rather than fixed.

6. Firm-Workers’ Joint Surplus (S_t(p)) The total present discounted value accruing to the firm-worker pair: firm profits per worker plus the contract value promised to workers. Because utility is transferable (risk neutrality) and the firm fully commits to its contract, this surplus depends only on the firm’s current productivity and the aggregate state — not on the promised contract value V. The surplus S_t(p) is the key object determining firm entry/exit (the firm continues if and only if S_t(p) ≥ U_t) and optimal hiring (the marginal return to an additional hire equals S_t(p) − V(p)).

7. Cleansing vs. Anti-Cleansing Firm Selection In models with endogenous firm entry and exit, a negative aggregate shock can either raise or lower the productivity threshold for firm survival. “Cleansing” refers to the standard mechanism where a negative productivity shock raises the exit threshold, selecting out low-productivity firms and improving the average quality of survivors. “Anti-cleansing” (as in the baseline multi-shock calibration) occurs when separation rate or hiring cost shocks lower the optimal wage contract and reduce the exit threshold, allowing less productive firms to survive and worsening average firm productivity.

The Geography of job creation and job destruction

Mon, 01 Jan 0001 00:00:00 +0000

This paper asks why unemployment rates differ so persistently across local labor markets, and what role job creation and job destruction play in generating those differences. The authors document a comprehensive set of spatial labor market facts using administrative and survey microdata from Germany, the United States, and the United Kingdom, then build and calibrate a quantitative theoretical framework that accounts for all documented regularities.

Data and scope. For Germany, the authors use administrative data from the German employment office (universe of vacancies and unemployed, 1999–2020) and the IAB social security sample (SIAB, 2% of all workers, 2000–2017) aggregated to 194 commuting zones. For the U.S., they use BLS Local Area Unemployment Statistics (2000–2019) at commuting zones, CPS worker flows at metropolitan areas, and JOLTS vacancy data for the 18 largest MSAs (covering roughly 40% of the U.S. labor force). For the UK, they use Nomis data and Jobcentre Plus vacancy records (2004–2006) for 378 Local Authority Districts.

Empirical findings. Spatial unemployment rate differences are large and highly persistent. In Germany, the correlation of local unemployment rates across commuting zones over a 19-year span is 0.84 (West) and 0.77 (East). In the U.S., the correlation between 2000 and 2019 unemployment rates is 0.81; in the UK it is 0.76. In all three countries, local labor markets with lower unemployment are tighter (more vacancies per unemployed worker) and less productive. Firms in low-unemployment markets fill vacancies more slowly — in Germany, vacancy duration ranges from approximately 35 days in high-unemployment locations to approximately 65 days in low-unemployment locations, roughly an 85% difference.

A formal steady-state decomposition reveals that across all three countries, differences in job-separation rates account for approximately two-thirds of the cross-sectional variation in unemployment rates, while differences in job-finding rates account for roughly one-third. Specifically: Germany 62.4% separations / 33.2% job-finding; U.S. 72.0% / 32.8%; UK 64.3% / 35.8%. This primacy of separation rates in the cross-section stands in stark contrast to business-cycle dynamics, where job-finding rates account for 50–60% of unemployment fluctuations (Fujita and Ramey, 2009).

Theory. The authors embed a Diamond-Mortensen-Pissarides (DMP) model with endogenous separations — following Den Haan, Ramey, and Watson (2000) — into a Rosen-Roback spatial equilibrium framework. Locations differ in exogenous productivity; workers and firms are freely mobile; cost-of-living differences sustain the spatial equilibrium. The model is calibrated to the U.S. median-unemployment labor market (separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365) plus the productivity differential between the 5th and 95th percentile unemployment locations (4.8% higher and 3.0% lower productivity than median, respectively). The baseline model, imposing the Hosios condition, matches the spatial patterns of separation rates, job-finding rates, tightness, vacancy duration, wages, and cost of living without targeting most of these. The decomposition in the calibrated baseline model attributes 33.5% of spatial unemployment variation to job-finding rates, compared to 32.8% in the data.

The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot explain why job-finding rates dominate business-cycle fluctuations. Introducing on-the-job search (with 12% of employed workers searching each period, calibrated from Faberman et al., 2017) resolves both problems. In the extended model, job-to-job transition rates are virtually constant across local labor markets (matching the data) but strongly procyclical over the business cycle. This asymmetry amplifies the response of vacancies and job-finding rates to aggregate productivity shocks while muting the cyclical variation in separation rates. The extended model’s business-cycle decomposition attributes 54.4% of unemployment volatility to job-finding rates, within the empirical 50–60% range.

Policy implications. Under the Hosios condition, the decentralized equilibrium is efficient — large spatial differences in unemployment, tightness, and wages are efficient outcomes, not signs of mismatch. The relevant policy benchmark is not deviation of tightness from the national average but deviation from the model’s location-specific prediction conditional on local productivity.

Q: What is the central empirical puzzle the paper addresses? A: Spatial unemployment differences are large and persistent — in Germany, unemployment rates ranged from 1.9% to 11.9% across commuting zones even after 15 years of decline. These differences are not well understood theoretically, and the crucial missing empirical piece was data on job creation and vacancy filling across locations, which this paper provides for three countries.

Q: How large and persistent are cross-sectional unemployment differences in each country? A: In Germany, commuting-zone unemployment ranged from 3.6% to 24.0% in 2000 and persisted with a 19-year correlation of 0.84 (West) and 0.77 (East). In the U.S., the 2000–2019 correlation is 0.81, with unemployment as low as 1.5% and as high as 16.9% in 2000. In the UK, the 2004–2018 correlation is 0.76, with 2004 unemployment ranging from 1.8% to 13.1%.

Q: What do the data show about the relationship between unemployment and labor market tightness across locations? A: In all three countries, lower-unemployment labor markets are tighter — they have more vacancies per unemployed worker. This is documented for Germany using the universe of registered vacancies, for the U.S. using JOLTS data for 18 large MSAs, and for the UK using Jobcentre Plus administrative data. The relationship holds after controlling for local labor market composition (age, gender, education, occupation, industry shares).

Q: What do vacancy-filling rates look like across locations, and how large are the differences? A: Vacancy-filling rates are lower in low-unemployment (tight) labor markets. In Germany, the monthly probability of filling a vacancy is approximately 50% higher in high-unemployment markets than in low-unemployment markets. Completed vacancy duration ranges from about 35 days in high-unemployment locations to about 65 days in low-unemployment locations — a difference of approximately 85%. The UK data show a strikingly similar elasticity of vacancy-filling rates with respect to unemployment rates to Germany.

Q: What does the formal decomposition reveal about the sources of spatial unemployment differences? A: In a steady-state two-state decomposition, separation rates account for 62.4% (Germany), 72.0% (U.S.), and 64.3% (UK) of cross-sectional unemployment variation, while job-finding rates account for 33.2%, 32.8%, and 35.8%, respectively, with small residuals. This consistently assigns primary importance to separation rates across all three countries.

Q: Why is the primacy of separation rates in the cross section surprising, and what literature does it contrast with? A: The business-cycle literature (Fujita and Ramey, 2009; Shimer, 2012) finds that job-finding rate variation accounts for 50–60% of unemployment fluctuations over the cycle, roughly twice the contribution of separation rates. The spatial pattern is the mirror image: separations dominate. Any credible theory of spatial unemployment must rationalize both patterns simultaneously — a challenge the paper explicitly takes up.

Q: How does the baseline DMP model with endogenous separations generate the spatial patterns? A: Higher-productivity locations feature higher match surpluses. Higher surplus induces more vacancy creation and tighter markets, raising job-finding rates and lowering vacancy-filling rates. Crucially, a higher surplus means idiosyncratic shocks must be more negative to make the joint surplus negative, so fewer matches dissolve — separation rates are lower. The calibrated model reproduces the 32.8% job-finding / ~67% separation decomposition without targeting it (model yields 33.5% job-finding).

Q: What are the calibration targets and key parameter values in the baseline model? A: The model is calibrated monthly to the U.S. economy. Median-unemployment-location targets: separation rate 0.0128, job-finding rate 0.2368, vacancy-filling rate 0.7365. Productivity targets: the 5th-percentile-unemployment location is 4.8% more productive than median, and the 95th-percentile-unemployment location is 3.0% less productive. Key calibrated values include matching elasticity alpha = 0.4711 (equal to worker bargaining power under Hosios), matching efficiency m = 0.4371, vacancy posting cost kappa = 0.3070, and flow nonmarket value z = 0.9072.

Q: What are the two shortcomings of the baseline model, and how does on-the-job search resolve them? A: The baseline model generates a counterfactual upward-sloping Beveridge curve and cannot generate the asymmetry between cross-sectional and business-cycle drivers of unemployment. Adding on-the-job search (fraction phi = 0.12 of employed workers searching, calibrated from Faberman et al., 2017) resolves both. It corrects the Beveridge curve by allowing the model to match the spatial vacancy-unemployment relationship, and it introduces procyclical job-to-job mobility that amplifies the cyclical response of job-finding rates while dampening cyclical separation rate variation.

Q: How do job-to-job transition rates differ across space versus over the business cycle, and why does this matter? A: Job-to-job rates are virtually constant across the cross-section of local labor markets (the extended model is calibrated to match this). But they are strongly procyclical — high in booms, low in recessions, about as volatile as job-finding rates over the cycle. In a boom, more employed workers search, spurring vacancy creation, which raises both vacancy-filling probability (making vacancies easier to fill) and job-finding probability for the unemployed, amplifying the cyclical job-finding rate response while muting the cyclical separation rate response.

Q: What does the extended model predict for business-cycle dynamics? A: The model with on-the-job search and aggregate productivity shocks (parameterized following Hagedorn and Manovskii, 2008) generates unemployment and vacancy rates that are an order of magnitude more volatile than productivity — matching the data. Labor market tightness is about twice as volatile as unemployment, as in the data. The Fujita-Ramey decomposition in the model attributes 54.4% of unemployment volatility to job-finding rates, which falls within the empirical range of 50–60%.

Q: What is the paper’s efficiency result and its policy implication? A: Under the Hosios condition (imposed in calibration), the decentralized equilibrium is efficient: job creation and destruction are privately efficient in each market, and free mobility of workers and firms ensures efficient spatial allocation. Therefore, large observed differences in unemployment, tightness, and wages across locations are not evidence of inefficiency. The relevant signal for policy is not deviation from the national average but deviation from the model’s location-specific prediction conditional on productivity. Locations where data deviate from model predictions are candidates for policy intervention.

Q: Do the spatial patterns survive controls for worker and firm composition? A: Yes. The authors regress labor market tightness and vacancy-filling rates on local unemployment rates and a full set of composition controls (age, gender, education, occupation, and industry shares) derived from the IAB microdata for Germany, along with year fixed effects. The relationship between local unemployment and both tightness and job-filling rates remains highly statistically and economically significant after these controls, for both Germany and the U.S.

Q: How does the model handle wages and cost of living, and does it match the data? A: Wages are determined by state-contingent generalized Nash bargaining with worker bargaining power eta. Cost-of-living differences are backed out as the values needed to sustain the spatial equilibrium (Rosen-Roback). Neither wages nor costs of living are calibration targets in the cross section, yet the model closely matches the empirically observed wage gradient across local labor markets and the negative correlation between cost of living and local unemployment (using Economic Policy Institute Family Budget Calculator data).

Labor market tightness: The ratio of vacancies posted in a local labor market to the number of unemployed workers in that market; the paper documents that tightness is systematically higher (more vacancies per unemployed worker) in lower-unemployment locations across all three countries.

Job-separation rate (EU rate): The share of employed workers who transition from employment to unemployment in a period; in the paper’s framework, this is endogenously determined by the idiosyncratic match productivity threshold below which the joint match surplus turns negative, and it is the primary driver of spatial unemployment differences (accounting for roughly two-thirds of cross-sectional variation).

Job-finding rate (UE rate): The share of unemployed workers who transition from unemployment to employment in a period; in the paper’s framework, this is higher in tighter (lower-unemployment) markets, but accounts for only roughly one-third of spatial unemployment variation — the opposite of its dominant role in business-cycle fluctuations.

Spatial Beveridge curve: The cross-sectional relationship between vacancy rates and unemployment rates across local labor markets; in the data it is downward sloping (low-unemployment locations have both high vacancies and low unemployment), which the baseline model fails to capture but the extended model with on-the-job search reproduces.

Endogenous separation threshold: The location-specific minimum idiosyncratic match productivity below which the joint match surplus becomes negative and the worker-firm pair dissolves; this threshold is lower (tolerates a wider range of idiosyncratic shocks) in higher-productivity locations because the average surplus is larger, generating lower separation rates in more productive locations.

Spatial equilibrium (Rosen-Roback): The equilibrium condition in which differences in local costs of living adjust to make workers and firms indifferent across locations, sustaining persistent productivity-driven differences in wages and unemployment as equilibrium outcomes rather than disequilibrium phenomena.

Procyclical on-the-job search: The mechanism by which the fraction of employed workers actively searching — and thus the rate of job-to-job transitions — is approximately constant across the cross-section of local labor markets but strongly procyclical over the business cycle. This asymmetry is the key to reconciling why job-finding rates drive business-cycle unemployment variation while separation rates drive spatial unemployment variation.

Hosios condition: The parametric restriction equating the unemployment elasticity of the matching function (alpha) and the workers’ Nash bargaining weight (eta); when satisfied, job creation is efficient in every local labor market. The paper imposes this condition deliberately to demonstrate that the decentralized equilibrium is efficient despite large spatial differences in outcomes.